Topological Defects: Threads, Walls, and Rings

[Leonid]

1. Thread topological defects and domain walls. In which cases these defects involve new items in Hamiltonians of models? The connection between thread topological defects and first-order phase transitions (for instance in the Nielsen-Olesen model, helium II, in which Chalatnikov quantum vortices appear, in type II superconductors). More exactly, it is known that all the kinds of topological defects imply breaking the thermodynamic equilibrium over the defect regions (in the coordinate space). In which agreement this fact is with above "defects" items in Hamiltonians and with the first-order phase transitions dynamics therein.
2. Ring vortices. Mit which a topological relation they are govern (I mein a relation between the \pi groups of the residual symmetry group space and the appropriate vacuum manifold at breaking the [gauge] symmetry). Is that the same relation as in the case of rectilinear vortices?

 

[zmike]

Thread topological defects and domain walls are special cases of topological defects that occur in many different models. They are associated with the breaking of a continuous symmetry in the Hamiltonian, resulting in a first-order phase transition. The connection between thread topological defects and first-order phase transitions is due to the fact that these defects cause a breaking of thermodynamic equilibrium over the defect regions, which leads to the formation of a new state of matter.

Ring vortices are also a type of topological defect, however, they are governed by a different topological relation than rectilinear vortices. This relation is between the $\pi$ groups of the residual symmetry group space and the appropriate vacuum manifold at the breaking of the gauge symmetry. This relation is not the same as that for rectilinear vortices, but instead it is related to the formation of a ring-like structure in the coordinate space.